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Phonon maximum frequency

Figure 2 Vibrational energy relaxation (VER) mechanisms in polyatomic molecules, (a) A polyatomic molecule loses energy to the bath (phonons). The bath has a characteristic maximum fundamental frequency D. (b) An excited vibration 2 < D decays by exciting a phonon of frequency ph = 2. (c) An excited vibration >d decays via simultaneous emission of several phonons (multiphonon emission), (d) An excited vibration 2 decays via a ladder process, exciting lower energy vibration a> and a small number of phonons, (e) Intramolecular vibrational relaxation (IVR) where 2 simultaneously excites many lower energy vibrations, (f) A vibrational cascade consisting of many steps down the vibrational ladder. The lowest energy doorway vibration decays directly by exciting phonons. (From Ref. 96.)... Figure 2 Vibrational energy relaxation (VER) mechanisms in polyatomic molecules, (a) A polyatomic molecule loses energy to the bath (phonons). The bath has a characteristic maximum fundamental frequency <x>D. (b) An excited vibration 2 < <x>D decays by exciting a phonon of frequency <x>ph = 2. (c) An excited vibration >d decays via simultaneous emission of several phonons (multiphonon emission), (d) An excited vibration 2 decays via a ladder process, exciting lower energy vibration a> and a small number of phonons, (e) Intramolecular vibrational relaxation (IVR) where 2 simultaneously excites many lower energy vibrations, (f) A vibrational cascade consisting of many steps down the vibrational ladder. The lowest energy doorway vibration decays directly by exciting phonons. (From Ref. 96.)...
A notable measure of the intermolecular forces is the maximum frequency v of the lattice vibrations (optical phonons). In a typical organic molecular crystal, it is of the order of 3.5 THz in Si, in contrast, it is 14THz. Thus the difference in the Boltzmann factors exp(-hv/feT) for the thermal occupation of phonon states, which plays a decisive role in many solid-state properties, is already great when comparing organic and inorganic solids at room temperature, and it becomes very much greater at low temperatures (Table 1.2). [Pg.11]

The highest frequency or energy of an external phonon is that of an optical phonon at K = 0. It has the value 3.9 THz or 16.1 meV. Compared to the optical phonon of Si at K = 0, these values are about a factor of 4 smaller. The width of the whole spectrum of the optical phonons is around 2.5 THz. Above the maximum frequency of 3.9 THz, the spectrum exhibits a gap which is about half as wide as the overall width of the spectrum of the optical phonons. The frequencies of the internal molecular vibrations are observed only above this gap. Their dispersion is weaker than that of the external modes. The gap in the spectrum, the number of phonon branches below... [Pg.102]

Qualitatively, the dynamic properties of different polyacene crystals are similar, since both the intermolecular van der Waals forces and also the molecular masses are to first order proportional to the number of C atoms per molecule. Therefore, for example all the sound velocities are of the same order of magnitude (Table 5.4). The same is true for the maximum frequencies of the optical phonons and of the intramolecular osdUations. A clear and general difference is however to be found between smaller and larger molecules in terms of the lowest frequencies of the intramolecular modes with increasing molecular mass, the frequency of the low-energy intramolecular vibrations shift towards lower values. These molecular excitations are either bending or torsional oscillations. This frequency shift can cause the gap and the strict separation of internal and external modes to become less sharp. [Pg.109]

This has been used for two-level tunnelling systems in insulating glasses. The coupling coefficient Fip from the phonon deformation potential should be independent of T and A, because the density of phonon modes in the Debye model is proportional to co up to the maximum frequency cod and this co-dependence counteracts the smaller overlap for larger A. The electron rate Re may therefore dominate the total rate at small values of A, while Rip may be faster for large A up to the Debye energy k T. ... [Pg.96]

The temperature dependence of non-radiative transitions, caused by linear diagonal and quadratic non-diagonal vibronic interactions, is also investigated on the basis of the non-perturbative quantum theory. It was found that the usual increase of the transition rate with temperature does not hold near some critical values of the non-diagonal interaction and temperature. At these critical values the rate is high (comparable to the mean phonon frequency) and its temperature dependence has a maximum. The results may be important for understanding the mechanisms of catalysis in chemical reactions. [Pg.151]

The thermostats for the wavefunction should not be coupled to the nuclear thermostats. Therefore, the value of the frequency parameter should be a few times larger than that of maximum of the phonon spectrum.2... [Pg.237]

As the value of Q continues to increase the centre of the Gaussian envelope moves out to higher frequencies and its width expands. The envelope s central intensity maximum decreases dramatically and the total intensity falls, since the Debye-Waller factor is smaller. Eventually the envelope will broaden and weaken to such an extent that it disappears into the experimental background. This simple picture nicely summarises the effects of phonon wings but it will be considerably modified by the introduction of more realistic treatments of the external vibrations of molecular crystals, see Chapter 5. However, the model remains sufficiently robust to provide an introduction to the effects of molecular recoil. [Pg.59]


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Phonon frequency

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